Some atoms are unstable. They have too much energy or the wrong mix of particles in the nucleus. So to make themselves more stable, they breakdown (or decay) and get rid of some matter and/or some energy. This is called radioactive decay and isotopes of atoms that do this are called radioisotopes.
The process is spontaneous and random. You can't do anything to speed it up or slow it down and you can't predict when it will happen. The only reason we can do any calculations on radioisotopes is because there are huge numbers of atoms in most samples so we can use statistics to accurately predict what's most likely to happen.
From what I got with my answer (8.192 cm) I went ahead and rounded it to the closest answer which is 12 cm. Hopefully im correct but if not, I apologize in advance.
